Formally, following the notation introduced in [1]}, [2]}, we define a domain \(\mathcal {D}\)  consisting of two components: a d-dimensional feature space \(\mathcal {X} \subset \mathbb {R}^d\)  and a marginal probability distribution \(P(X)\) , where \(X = \lbrace x_1, \dots , x_n\rbrace  \subset \mathcal {X}\) . Given a specific domain, \(\mathcal {D} = \lbrace \mathcal {X}, P(X)\rbrace \) , we formulate a task \(\mathcal {T}\) defined by a label space \(\mathcal {Y}\)  and the conditional probability distribution \(P(Y|X)\) , where \(Y = \lbrace y_1, \dots , y_n\rbrace \)  is the set of the corresponding labels for \(X\) . In general, \(P(Y|X)\)  can be learned in a supervised manner from these feature-label pairs \(\langle x_i, y_i \rangle \) .
